My family has been enjoying Tang Math card games. I purchased two sets, “Home Kit Jr.” for K–2 and “Home Kit Sr.” for grades 3–5. (You can also buy the decks singly, but I think that’s a bad deal.) These are great as math exercises; they are less fun but okay as games.
The basic idea of Kakooma is to look at a grid of five or nine numbers and find two numbers than sum (or multiply) to a third. Numtanga shows numbers or values written in different ways; the idea is to find matching numbers on two different cards.
My favorite game is Expresso. A card shows four numbers. You role a die. Then, using two to four of the numbers (or three or four of the numbers with the harder cards), you figure out a way to add, subtract, multiply, or divide to reach the value on the die. This can get quite challenging.
What we did is just go around in a circle with everyone taking a turn solving an Expresso puzzle. You can also make this competitive my seeing who can find a successful solution first, but generally that would favor the person fastest at finding such patters, so I don’t think that would be much fun.
Here’s another way to make the game harder and more competitive: Take turns, but each player tries to find as many solutions for each card and die roll as possible. Then, the player with the most successful solutions wins the card. In cases of a tie, the person whose turn it is (or who is next in line) wins the tie.
The dice game Yatzee is great for older children to work on sums. But what about younger children? Yahtze is just too complicated for those just starting out with math. I toyed with the idea of modifying Yahtzee for younger children but came up blank. But then I hit upon a simple two-dice game that my five-year-old has enjoyed.
My kid loves Magformers, plastic shapes with magnets embedded. He plays with them as toys; I appreciate them because they promote spacial reasoning. You can build squares into cubes, triangles into pyramids, and combined shapes into many complex 3D figures.
They are a bit expensive. I got lucky and bought multiple sets from a family off of CraigsList. One of the sets we got has specialized shapes for building dinosaurs. My son enjoys building the dinosaurs but I don’t consider those packs essential. (Magformers offers many other sorts of packs that can get quite expensive.) If I were going to buy sets new, I’d go with a basic starter pack plus perhaps a gear pack (paid links).
As adults, digit placement is second nature: ones, tens, hundreds, thousands, etc. It’s easy to forget that the way we now use numbers was an important cultural invention. And it’s easy to forget how hard it was to learn digits as a child. One of my biggest surprises as a homeschooling dad of a kindergarten-age child has been seeing what a conceptual leap it is to grasp digit placement. It helps enormously for kids to see visually what we’re talking about.
Of course it’s easy to make groupings of ten coins or whatever. I’ve used wooden cube blocks to illustrate two-digit numbers. But doing ten stacks of ten, and then ten stacks of a hundred, can be a challenge. That’s where Perler beads and pegboards (paid links) come in. You can get a large set for around thirty bucks and then iron together sets of ten and a hundred. (Or you can save some effort and spend over a hundred bucks on Montessori “golden beads” (paid link) if you prefer. There’s also a lower-cost foam option (paid link).) You can also do art projects with the Perler beads if you’re so inclined.
Update, June 28, 2021: Although I do like the Perler beads for visualizing big numbers, practically speaking, I turned to the foam blocks for routine instruction. To my mind these are a must-have item for beginning math students. The beads are a little too small for counting; the blocks are just right. It occurred to me that you could also just buy a jumbo pack of wood blocks and glue them together into rows of ten and squares of a hundred. But the foam blocks come cheap and ready-made.
I was working with my five-year-old in Dimensions math, and we came across an exercise that asks the students to circle all of the circles shown. Some of the shapes represent cylinders; one represents a football. Obviously the top and bottom of a cylinder are circles. But what about a football? This led to an interesting discussion about dimensions.
My five-year-old had fun playing with foam sheet triangles I cut out—and we even introduced Pythagoras’s theorem for right triangles.
I was inspired by some sample materials offered by Math Expressions (start on page 14 of this pdf). One thing this source recommends is to discuss the difference between “turning” a triangle piece and “flipping” the piece.
Raising a child helps you remember just how hard it was to learn certain things. Most kids pick up counting to ten without much problem (after they learn to talk). But grasping double-digit numbers (and beyond) is a greater conceptual challenge. Now you have to be able to count groups of ten (and then groups of a hundred, and so on) and represent them with digit placement. Later on, multiplication (and then exponents) build on a child’s earlier conceptual knowledge.
I’ve found that a pack of wooden cubes can help illustrate the relevant concepts nicely. When a child can see, for example, two sets of ten blocks, plus three extra blocks, the child can more-readily grasp the number 23. One issue I’ve seen is confusion about the number 23 versus the addition of 2 and 3; the difference is very easy to show with blocks. Of course the blocks are also really good for practicing simple addition and subtraction.
I absolutely love DragonBox math game apps. They make math concepts intuitive and fun. My brother used them for his kids and sang their praises, so I got them too. Here I review the four apps aimed at children ages 4 to 9: Numbers, Big Numbers, Algebra 5+, and Magnus’ Kingdom of Chess. The company also has apps for advanced algebra and for geometry; I’ll buy those down the road when my child is ready for them. The app is available for various devices; here I provide links to Amazon for those with suitable Amazon devices.
My five-year-old is not ready to add mixed fractions. But, by using a fraction wheel, he is already beginning to grasp, intuitively, how fractions work.
Just today, I got out the fraction wheel pieces, and he said he wanted to “build them” himself. He put a half-piece together with a third-piece, then tried to complete the circle. He tried a fourth-piece—too big. Then an eighth-piece—too small. He could see right away, once he tried it, that a sixth-piece added to a third-piece equals a half. He didn’t need to know how to formally convert one-third to two-sixths for this, but he could see visually that one-third equals two-sixths. He also immediately saw that three sixth-pieces are a half and six of them are a whole.
Obviously I’m not going to try to teach him formal fraction conversions until he has a better handle on the four basic operations (addition, subtraction, multiplication, and division). But I think this early work with the fraction wheel set will put him in good shape to grasp adding and subtracting complex fractions later on.
I know there are some really well-crafted fraction wheels with little handles on the pieces; the disadvantage of these is that you can’t stack pieces on top of each other.
My wife and I created a simple fraction wheel set that you’re free to download. For best results, print these out using different colors of paper and then glue them to card stock or cardboard, or just print them out on cardstock if your printer can handle that. Or, as I discuss in my post about triangles, you can use foam sheets, although you probably won’t be able to print the patterns directly onto the foam sheets.